Impedance Spectroscopy Properties of Pr_{0.67}A_{0.33}MnO_{3} (A = Ba or Sr) Perovskites
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DOI: 10.1007/s10948-013-2240-2
- Cite this article as:
- Hcini, S., Khadhraoui, S., Triki, A. et al. J Supercond Nov Magn (2014) 27: 195. doi:10.1007/s10948-013-2240-2
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Abstract
We have investigated the dielectric properties of Pr_{0.67}Ba_{0.33}MnO_{3} (PBMO) and Pr_{0.67}Sr_{0.33}MnO_{3} (PSMO) perovskites synthesized by the solid-state reaction method at 1473 K. Samples were characterized by complex impedance spectroscopy (CIS) in the frequency range from 40 Hz to 1 MHz, at room temperature. The conductivity curves for the two samples were well fitted by the Jonscher law σ(ω)=σ_{dc}+Aω^{n}. For the PBMO sample, the hopping process occurs at long distance, whereas for PSMO compound it occurs between neighboring sites. Frequency dependence of dielectric constant (ε″) and tangent loss (tanδ) show a dispersive behavior at low frequencies that was explained on the basis of the Maxwell–Wagner model and Koop’s theory. Electric modulus formalism has been employed to study the relaxation dynamics of charge carriers. For both compounds, the variation of the imaginary part Z″ shows a peak at a relaxation angular frequency (ω_{r}) related to the relaxation time (τ) by τ=1/ω_{r}. Nyquist plots of impedance show the presence of two semicircles and an electrical equivalent circuit has been proposed to explain the impedance results.
Keywords
PerovskitesDielectric propertiesImpedance spectroscopyGrains and grain boundaries effects1 Introduction
Perovskite manganese oxides, Ln_{1−x}A_{x}MnO_{3} (Ln = rare earth, A= Ca, Sr, Ba, etc.) have been extensively studied in the last years due to their interesting properties, which suggest the possibility of applications in diverse technology areas. The various physical properties of these perovskites materials are highly influenced by many factors such as the method of synthesis, the doping level in the A-site [1], the average ionic radius of A-site [2], the deficiency of oxygen [3], grains and grain boundaries effects [4, 5], etc. These materials are interesting in the electrochemical applications such as air electrodes in solid oxide fuel cells (SOFC) [6], in the magnetic refrigeration applications [7, 8], and in electronic technologies such as magnetic recording at high density and high-sensitivity magnetic sensors [9, 10].
A way to control the dielectric properties of perovskites materials can be achieved by the complex impedance spectroscopy (CIS). Along this line, several studies have been reported in the literature in order to understand the nature of electrical conduction process in these materials [11–13].
Recently, we have studied the structure, and the magnetic and electrical properties of Pr_{0.67}Ba_{0.33}MnO_{3} (PBMO)^{1} and Pr_{0.67}Sr_{0.33}MnO_{3} (PSMO) perovskites [5]. Both compounds exhibit a transition from a paramagnetic-insulator (PMI) to a ferromagnetic-metallic (FMM) states. We have also shown in our recent work [14], using the percolation model that the observed metal-insulator (M-I) transition in our samples can be due to a percolation of FMM domains.
The objective of the present work is to compare the dielectric and ac-conduction properties of PBMO and PSMO compounds over the wide range of frequencies at room temperature. Conductivity, dielectric, and complex impedance properties of our materials can be determined and interpreted from the CIS, which is an important and powerful technique to study the dielectric and conduction properties of materials.
2 Experimental
Polycrystalline samples were prepared using solid-state reaction at 1473 K. Microstructure analysis, M(T) and ρ(T) measurements were reported in our previous work [5]. The dielectric properties were examined by an impedance analyzer (Novocontrol Alpha-analyzer) over a broad frequency range (40 Hz–1 MHz) at room temperature. In the impedance analyzer, the sintered disk with a diameter of 10 mm and a thickness of approximately 2 mm was placed between two gold parallel electrodes.
3 Electrical Conductivity Studies
- (i)In the plateau region, the conductivity (σ_{dc}) is higher for PSMO than that for PBMO as clearly shown in Fig. 1 and their values are compared in Table 1. This result indicates that the conduction process is more activated for PSMO than that for PBMO. This difference in σ_{dc} for the two compounds may be related to the prominent role of the grain boundary in PBMO which decreases the double exchange coupling (DEC) of Mn^{3+}–O^{2−}–Mn^{4+} and in turn makes the PBMO sample lesser conductor as compared with PSMO [5].Table 1
The best fitting parameters obtained from experimental data of the conductivity as a function of frequency using the Jonscher power law σ(ω)=σ_{dc}+Aω^{n}
σ(ω)=σ_{dc}+Aω^{n}
Sample code
σ_{dc}×10^{−3}
A×10^{−10}
n
R^{2}
PBMO
2.67
851.9
0.772
0.985
PSMO
15.03
5.202
1.206
0.992
- (ii)In Fig. 1, the variation of (σ_{ac}) at high frequencies (ω>10^{5} Hz) occurs with changes in the slope and can be described by the power law [15–17]:where A is the preexponential factor and n is the power law exponent. The exponent n represents the degree of interaction between mobile ions with the lattice and the coefficient A determines the strength of polarizability.$$ \sigma_{ac}(\omega) = A\omega^{n}, $$(6)
Equation (7) is used to fit the conductivity data for PBMO and PSMO samples. In the fitting procedure, the A and n values have been varied simultaneously to get the best fits. One can see that the fitting was perfectly matched with the measured values. The representative nonlinear fitting curves and the calculated values are given in Fig. 1 and Table 1, respectively. The goodness of fit is usually evaluated by comparing the squared coefficient of linear correlation coefficient (R^{2}) (see Table 1).
4 Dielectric Studies
Due to higher resistance offered by the grain boundaries at low frequencies more energy is required for the motion of charge carriers, and hence the energy loss (tanδ) is also high in this frequency range (see Fig. 3b). On the other hand, at high frequencies as low resistance is offered by grains less energy is required by the charge carriers for motion so the dielectric loss is low.
5 Electrical Modulus Analysis
The variations of imaginary part of electrical modulus M″ with frequency at room temperature are shown in Fig. 4b from which we can note that the position of the relaxation peaks shift toward higher frequencies from PBMO to PSMO, thus providing means for the study of relaxation. Consequently, this means that relaxation rate for this process increases from PBMO to PSMO. The low-frequency side of the imaginary part of modulus determines the range in which charge carriers are mobile on long distances (the charge carriers represent the possibility of the ion migration via hopping from one site to the neighboring site). At high frequency, above the peak (maximum of M″), the carriers are spatially confined to potential wells, being mobile on short distances, and thus could be made to have localized motion within the well.
6 Complex Impedance Analysis
The merge in curves of Z′ in the higher frequency region for the two samples is probably due to the release of space charges as a result of reduction in the barrier properties of the material at room temperature and can be interpreted by the presence of space charge polarization.
The impedance data are fitted using Zview software and the best fit (green solid line in Fig. 6) is obtained when employing an equivalent circuit formed by a resistance R_{1} (grain resistance R_{g}) in series with a parallel combination of resistance R_{2} (grain boundary resistance R_{gb}) and constant phase element impedance (Z_{CPE}). The equivalent configuration is of the type [R_{1}+(R_{2}//Z_{CPE})], as shown in the inset of Fig. 6.
- (i)
capacitance when p=1.
- (ii)
warburg impedance when p=0.5.
- (iii)
simple resistance when p=0.
Electrical parameters of equivalent electrical circuit deduced from complex impedance spectrum for PBMO and PSMO samples
Sample code | R_{1}=R_{g} (kΩ) | R_{2}=R_{gb} (kΩ) | T (nF) | p |
---|---|---|---|---|
PBMO | 413.9 | 698.9 | 0.987 | 0.81 |
PSMO | 152.0 | 532.5 | 11.20 | 0.83 |
Table 2 shows also that the grain boundary resistance R_{2}, is lower for PSMO than for PBMO. It seems to be due to the fact that the grain boundary effect has assisted in lowering the barrier to the motion of charge carriers paving the way for increased electrical transport with rise in temperature.^{4} The evidences of grain boundary conduction have been observed in perovskites ceramic, ceramic conductors, and also in ceramic dispersed ionically conducting composite polymers [35–37].
7 Conclusion
We have investigated in this work the dielectric properties of PSMO and PBMO samples using complex impedance spectroscopy at room temperature. Electrical conductivity curves are found to obey Jonscher universal power law. The hopping process occurs at long distance for PBMO sample and between neighboring sites for PSMO compound. Frequency dependence of dielectric constant (ε″) and tangent loss (tanδ) at room temperature indicate a dispersive behavior at low frequencies. The relaxation dynamics of charge carriers for our samples has been studied using the modulus spectra. Complex impedance analysis indicates that the dielectric properties of the materials are strongly dependent on frequency and can be described as grains and grain boundary media. Impedance spectrum is characterized by the appearance of semicircle arcs which are well modeled in terms of electrical equivalent circuit with a grain resistance (R_{g}) in series with a parallel combination of grain boundary resistance (R_{gb}) and constant phase element impedance (Z_{CPE}). The values of R_{g} and R_{gb} are lower for PSMO than for PBMO which confirms that PSMO is more conductive than PBMO.